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# Definition of Similar Figures

• Similar figures are figures that have the same shape but not necessarily the same size.

Examples of Similar Figures

• The trapezoids shown below are similar; they have the same shape but they are different in size.

• Any two corresponding sides in two similar figures have a common ratio called the scale factor.

The trapezoids ABCD and EFGH shown above are similar. So, .

• The ratio of areas of two similar figures is the square of the scale factor.
• The ratio of volumes of two similar figures is the cube of the scale factor.

### Solved Example on Similar Figures

Find the value of x, if the figures are similar.

Choices:

A.

B.

C.

D.

Step 1: Since the figures are similar, the ratios of the lengths of corresponding sides of the figures are equal.

Step 2:  [Write the proportion.]

Step 3:   [Substitute the values.]

Step 4: 12 × x = 5 × 6 [Write the cross products.]

Step 5:  [Divide both sides by 12.]

Step 6:  [Simplify.]

Step 7:  [Convert improper fraction into mixed number.]

Step 8: The value of x is .